How can I orbit precisely in the 3D viewport?
The simplest way I found to do this is to first snap your 3D cursor to the center of the object you want to pivot around, then change your Transform Pivot Point to 3D Cursor. Next, select the object you want your view centered on, and press Numpad . to center your view upon that object, then press Ctrl + Alt + Numpad 0 to center the active camera on your current view. Next, turn on Increment Snapping and open the settings for it. Under the Affect section, Make sure Rotate is the only option activated. Now make sure the active camera is currently selected, and press r, z, and then move the mouse. The view will snap at 5 degree increments. I don't know how to do this any other way, nor how to change the increments of the snapping.